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4*sin(t)^(2)

Derivative of 4*sin(t)^(2)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
     2   
4*sin (t)
$$4 \sin^{2}{\left(t \right)}$$
d /     2   \
--\4*sin (t)/
dt           
$$\frac{d}{d t} 4 \sin^{2}{\left(t \right)}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of sine is cosine:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
8*cos(t)*sin(t)
$$8 \sin{\left(t \right)} \cos{\left(t \right)}$$
The second derivative [src]
  /   2         2   \
8*\cos (t) - sin (t)/
$$8 \left(- \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}\right)$$
The third derivative [src]
-32*cos(t)*sin(t)
$$- 32 \sin{\left(t \right)} \cos{\left(t \right)}$$
The graph
Derivative of 4*sin(t)^(2)